Bags are a craft-able piece of apparel that allow the player to hold more Tools, Items and Armor.
There are currently 9 bags in game.
Here they are in order of smallest to biggest.The Leaf Bag holds the least (little space but still better than nothing), and the God Bag (formerly infinite space, then nerfed to 3000, currently even less) holds the most. As of now, the Shelly Bag is the best Bag.
All the bags used to be able to hold so much more, but Soybeen nerfed them a lot. Now, even the God Bag isn't that OP anymore (about 1000 space only now). You don't require a Bag to hold stuff because if you had no space then you wouldn't be able to grow. Bags are only increasing the amount of stuff you can hold. If you are not wearing a bag, you have 50 room. (armor tools and other items that you can wear/ equip do not take up any space in your inventory but on death, you will lose all of those items that you have crafted.)
Note: Bags don't drop upon death. They remain equipped by the player. However the player does lose Bags when he rebirths (the player can't escape rebirthing with a God Bag as the player can't drop it in a chest before rebirth.
Also the capacity of some bags got doubled in the Void Update (30/6/2018)